Solving x² + bx + c = 0, step by step
Factor it, then use the one fact that finishes it: a product is zero only when one of its factors is zero.
The question
(x + 9)(x + 8) = 0
(x + 9)(x + 8) = 0
(x + 9)(x + 8) = 0
x + 9 = 0orx + 8 = 0
x + 9 = 0→x = −9
x + 8 = 0→x = −8
x = −9orx = −8
- The left side is already a product of two brackets, and the right side is zero. That is the useful shape, so no factoring is needed here.
- Now the step that gives the answers: a product is zero ONLY when one of the things being multiplied is zero. Two numbers that multiply to zero — one of them has to be zero. So either (x + 9) is zero, or (x + 8) is zero.
- Solve each one. x + 9 = 0 gives x = −9, and x + 8 = 0 gives x = −8. Notice the sign turns over: a + in the bracket gives a NEGATIVE answer.
- So x = −9 or x = −8. Either one makes the equation true, and it is "or" rather than "and" — x cannot be both at once.
How it works.
- 01
The left side is already a product of two brackets, and the right side is zero. That is the useful shape, so no factoring is needed here.
- 02
Now the step that gives the answers: a product is zero ONLY when one of the things being multiplied is zero. Two numbers that multiply to zero — one of them has to be zero. So either (x + 9) is zero, or (x + 8) is zero.
- 03
Solve each one. x + 9 = 0 gives x = −9, and x + 8 = 0 gives x = −8. Notice the sign turns over: a + in the bracket gives a NEGATIVE answer.
- 04
So x = −9 or x = −8. Either one makes the equation true, and it is "or" rather than "and" — x cannot be both at once.